Question: Solve for $x$ : $4\sqrt{x} - 5 = 7\sqrt{x} + 6$
Solution: Subtract $4\sqrt{x}$ from both sides: $(4\sqrt{x} - 5) - 4\sqrt{x} = (7\sqrt{x} + 6) - 4\sqrt{x}$ $-5 = 3\sqrt{x} + 6$ Subtract $6$ from both sides: $-5 - 6 = (3\sqrt{x} + 6) - 6$ $-11 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{-11}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $-\dfrac{11}{3} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.